Let's solve this inequality step by step. We are given the inequality `2 - x > x^2`.

First, let's move all the terms to one side of the inequality: `2 - x - x^2 > 0`. Rearranging the terms, we get: `-x^2 - x + 2 > 0`.

Now, let's find the roots of the quadratic equation `-x^2 - x + 2 = 0` using the quadratic formula: `x = (-b ± √(b^2 - 4ac)) / (2a)`, where `a = -1`, `b = -1`, and `c = 2`.

Substituting these values into the quadratic formula, we get: `x = (1 ± √(1 + 8)) / (-2)`. Solving for `x`, we find that the roots of the quadratic equation are `x = -2` and `x = 1`.

Since the coefficient of the `x^2` term is negative, the parabola opens downward. This means that the inequality `-x^2 - x + 2 > 0` is satisfied for values of `x` between the roots `-2` and `1`.

Therefore, the solution to the inequality `2 - x > x^2` is **-2 < x < 1**.